Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session AAA05: V: Quantum Machine Learning
12:30 PM–2:30 PM,
Wednesday, March 22, 2023
Room: Virtual Room 5
Sponsoring
Unit:
DQI
Chair: Ryan Sweke, IBM Quantum
Abstract: AAA05.00006 : Renormalisation Through The Lens Of QCNNs*
1:30 PM–1:42 PM
Presenter:
Nathan A McMahon
(Friedrich-Alexander University Erlangen-Nurnberg)
Authors:
Nathan A McMahon
(Friedrich-Alexander University Erlangen-Nurnberg)
Petr Zapletal
(University of Erlangen-Nuremberg)
Michael J Hartmann
(Friedrich-Alexander-Universität Erlangen-Nürnberg)
Unlike most neural networks, the function of the QCNN used here is relatively straightforward to explain. First, each layer of the QCNN performs a process analogous to both renormalisation and quantum error correction. Then second, the remainder of the circuit simply determines if we are in the ground state of a stabiliser Hamiltonian. If the energy is sufficiently low we consider this to be in the target phase.
This QCNN also has a second feature, it is exactly equivalent to a constant depth quantum circuit + post-processing. Beyond just providing a cheaper circuit, this also points to the generalisation of phase recognising QCNNs beyond the cluster-ising model. Combining these with the fidelity view of quantum phases, I will discuss the potential of phase recognising QCNNs as a quantum information theory construction of renormalisation and phase transitions, as well as how this approach may be extended to transitions arising from incoherent errors.
*This work was supported by the EU program H2020-FETOPEN project 828826, NAM is also funded by the Alexander von Humboldt foundation.
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